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If $A$ is a square matrix of order $n$ then |adj$A$| is

\[\begin{array}{1 1}(1)|A^{2}| &(2) |A|^{n}\\ (3)|A|^{n-1}&(4)|A|\end{array}\]

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$A(adj A) = (adj A )A =|A|$
$A (adj A) =\begin{bmatrix} |A| & 0 & 0 & ... & 0\\ 0 & |A| & 0 & ... & |A| \\ ... & ... & ... & ... \\ 0 & 0 & ... & ... & |A| \end{bmatrix}$
$A (adj A) =\begin{vmatrix} |A| & 0 & 0 & ... & 0\\ 0 & |A| & 0 & ... & |A| \\ ... & ... & ... & ... \\ 0 & 0 & ... & ... & |A| \end{vmatrix}$
$|A| |adj A|=|A|^n$
$|adj A| =|A|^{n-1}$
Hence 3 is the correct answer.
answered May 2, 2014 by meena.p
 

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